How to get "Correct uv" to work on popup menu
Haven't had time to test this, the code comes from another answer.  Adds a menu label for each operator in the window_manager list of reg'd operators used.  The settings used for the Edge Slide operator are expanded. Added the correct_uv for you to test if changing the prop from the menu results in the behaviour you require.

import bpy
from bpy.props import BoolProperty

class SimpleCustomMenu(bpy.types.Menu):
    bl_label = "Recently Run Operators"
    bl_idname = "OBJECT_MT_simple_custom_menu"

    def draw(self, context):
        layout = self.layout
        wm = context.window_manager
        op = wm.last_edge_slide
        if op:        
            row = layout.row()
            row.prop(wm, "set_correct_uv")
            row.prop(op, "correct_uv")
            layout.separator()
        # reverse order
        ops = [o for o in wm.operators]
        ops.reverse()
        for o in ops:
            row = layout.row()
            row.label(text=o.name)
            if o.name == 'Edge Slide':
                layout.separator()
                row = layout.row()
                row.label(text="bpy.ops.transform.edge_slide(%s)" % ", "
                         .join(["%s=%s" % (k, str(v)) 
                                for k, v in o.properties.items()]))
                for k, v in o.properties.items():
                    row = layout.row()
                    row.label(text="%s = %s" % (k, str(v))) 
                # draw the prop
                row = layout.row()
                row.prop(o, "correct_uv")       
                layout.separator()

def get_correct_uv(self):
    op = self.last_edge_slide
    if op:
        return op.correct_uv
    return False

def set_correct_uv(self, value): 
    op = self.last_edge_slide   
    if op:
        op.correct_uv = value
    return None

def get_last_edgeslide(self):
    ops = [o for o in self.operators if o.name.startswith("Edge Slide")]
    if len(ops):
        op = ops[-1]
        return op
    return None

def register():
    bpy.types.WindowManager.last_edge_slide = property(get_last_edgeslide)

    bpy.types.WindowManager.set_correct_uv = BoolProperty(get=get_correct_uv,
                                                             set=set_correct_uv,
                                                             name="Set Correct UV")

    bpy.utils.register_class(SimpleCustomMenu) 


def unregister():
    bpy.utils.unregister_class(SimpleCustomMenu)


if __name__ == "__main__":
    register()

    # The menu can also be called from scripts
    bpy.ops.wm.call_menu(name=SimpleCustomMenu.bl_idname)


Narrow down the operator list above to the last occurrence of the Edge Slide operator, can also look at context.active_operator



Added a property on the window_manager with a getter and setter to emulate the operator property, and a last_edge_slide property on the window manager to return the last used edge slide op, or None.